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This paper investigates the robust stabilisation of a class of fractional-order non-linear systems via fixed-order dynamic output feedback controller in terms of linear matrix inequalities (LMIs). The systematic stabilisation algorithm…

Optimization and Control · Mathematics 2019-06-06 Elyar Zavary , Mahdi Sojoodi

This paper explores stability properties of periodic solutions of (nonlinear) fractional-order differential equations (FODEs). As classical Caputo-type FODEs do not admit exactly periodic solutions, we propose a framework of…

Systems and Control · Electrical Eng. & Systems 2026-05-28 Paul-Erik Haacker , Remco I. Leine , Renu Chaudhary , Kai Diethelm , André Schmidt , Safoura Hashemishahraki

In this paper, we address the inverse problem in the case of linear-quadratic discrete-time dynamic non-cooperative games. Given feedback laws of players that are known to be a Nash equilibrium pair for a discrete-time linear system, we…

Optimization and Control · Mathematics 2024-07-19 Emin Martirosyan , Ming Cao

Fractional diffusion equations replace the integer-order derivatives in space and time by their fractional-order analogues. They are used in physics to model anomalous diffusion. This paper develops strong solutions of space-time fractional…

Probability · Mathematics 2016-12-19 Zhen-Qing Chen , Mark M. Meerschaert , Erkan Nane

The paper studies the highly prototypical Fictitious Play (FP) algorithm, as well as a broad class of learning processes based on best-response dynamics, that we refer to as FP-type algorithms. A well-known shortcoming of FP is that, while…

Optimization and Control · Mathematics 2015-04-21 Brian Swenson , Soummya Kar , Joao Xavier

We consider dynamic cooperative games, where the worth of coalitions varies over time according to the history of allocations. When defining the core of a dynamic game, we allow the possibility for coalitions to deviate at any time and…

Computer Science and Game Theory · Computer Science 2017-04-04 Ehud Lehrer , Marco Scarsini

This paper is about a set-based computing method for solving a general class of two-player zero-sum Stackelberg differential games. We assume that the game is modeled by a set of coupled nonlinear differential equations, which can be…

Optimization and Control · Mathematics 2019-09-10 Xuhui Feng , Mario E. Villanueva , Boris Houska

In the present study, a numerical method, perturbation-iteration algorithm (shortly PIA), have been employed to give approximate solutions of nonlinear fractional-integro differential equations (FIDEs). Comparing with the exact solution,…

Numerical Analysis · Mathematics 2016-07-28 Mehmet Senol , I. T. Dolapci

This paper investigates the robust stabilisation of a class of fractional-order non-linear systems via fixed-order dynamic output feedback controller in terms of linear matrix inequalities (LMIs). The systematic stabilisation algorithm…

Optimization and Control · Mathematics 2019-06-05 Elyar Zavary , Mahdi Sojoodi

We consider a Mean Field Games model where the dynamics of the agents is subdiffusive. According to the optimal control interpretation of the problem, we get a system involving fractional time-derivatives for the Hamilton-Jacobi-Bellman and…

Analysis of PDEs · Mathematics 2018-01-23 Fabio Camilli , Raul De Maio

Neural differential equation models have garnered significant attention in recent years for their effectiveness in machine learning applications.Among these, fractional differential equations (FDEs) have emerged as a promising tool due to…

Machine Learning · Computer Science 2025-03-21 Wenjun Cui , Qiyu Kang , Xuhao Li , Kai Zhao , Wee Peng Tay , Weihua Deng , Yidong Li

Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…

Numerical Analysis · Mathematics 2022-04-11 Kai Diethelm

We investigate a two-player zero-sum differential game with asymmetric information on the payoff and without Isaacs condition. The dynamics is an ordinary differential equation parametrised by two controls chosen by the players. Each player…

Optimization and Control · Mathematics 2015-07-30 Rainer Buckdahn , Marc Quincampoix , Catherine Rainer , Yuhong Xu

We deal with coalitional games possessing strictly positive values. Individually rational allocations of such a game has clear fractional interpretations. Many concepts, including the long-existing core and other stability notions more…

Theoretical Economics · Economics 2023-04-24 Jian Yang

The following document presents a possible solution and a brief stability analysis for a nonlinear system, which is obtained by studying the possibility of building a hybrid solar receiver; It is necessary to mention that the solution of…

Numerical Analysis · Mathematics 2024-04-25 A. Torres-Hernandez , F. Brambila-Paz , P. M. Rodrigo , E. De-la-Vega , C. C. Calabrese

It is well known that a non-cooperative game may have multiple equilibria. In this paper we consider the efficiency of games, measured by the ratio between the aggregate payoff over all Nash equilibria and that over all admissible controls.…

Computer Science and Game Theory · Computer Science 2025-08-20 Jianfeng Zhang

We generalize the Bush--Mosteller learning, the Roth--Erev learning, and the social learning to include mistakes such that the nonlinear replicator-mutator equation with either additive or multiplicative mutation is generated in an…

Physics and Society · Physics 2023-12-05 Suman Chakraborty , Ishita Agarwal , Sagar Chakraborty

We consider some reaction-diffusion equations describing systems with the nonlocal consumption of resources and the intraspecific competition. Sharp conditions on the coefficients are obtained to ensure the stability and instability of…

Analysis of PDEs · Mathematics 2024-09-06 Yuming Chen , Vitali Vougalter

This paper is focused on local and global stability of a fractional-order predator-prey model with habitat complexity constructed in the Caputo sense and corresponding discrete fractional-order system. Mathematical results like positivity…

Dynamical Systems · Mathematics 2019-06-05 Shuvojit Mondal , Milan Biswas , Nandadulal Bairagi

This paper deals with the design of Fractional Order Proportional Integral (FO-PI{\lambda}) controller for the speed control of DC motor. A mathematical model of DC motor control system is derived and based on this model fractional order…

Systems and Control · Computer Science 2014-02-07 N. N. Praboo , P. K. Bhaba